Microscopic Selection Principle for a Diffusion-Reaction Equation
نویسندگان
چکیده
We consider a model of stochastically interacting particles on 2~, where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate 7/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V(7,) then satisfies 7 ~/2V(Y)~ ~/2 as y . oo. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor },~/2 and letting y ~ oo. This density solves the reaction-diffusion equation u, = 89 + u(1-u) , and under Heaviside initial data converges to a traveling wave moving at the same rate , f i .
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